The scientific selection of combinations from a field of choice yields a mathematical series for which formulated tables are available.
There are numerous uses to be made of combination selections such as arranging duty rotation rosters of a selected number of shift workers from an available field of eligible workers, so as to ensure fair rotation of the workers in a shift or in statistical research selecting sets of subjects from a large population.
Another, and much more widespread field of activity is in the selection of numbers for lottery tickets. Such selections are frequently carried out on a random basis. The use of mathematical combinational analysis enables systematic choices to be made, increasingly considerably the chances to obtain a prize.
The legalization of lotteries has become widespread, on the North American continent and elsewhere. In formulating lottery tickets on a systematized basis it is fairly usual to select a limited field of numbers, possibly chosen at random, within the scope of the lottery. From this elected field a predetermined number of "picks", as specified for that lottery is required for each lottery ticket that is to be completed.
As an example, in a "6/49" Lottery each ticket comprises a combination of six different numbers, selected in the range 1 through 49. Evidently, the total number of combinations of six numbers to be formulated between 1 and 49 runs into millions of combinations (13,983,816), it being practically impossible to complete such a large number of tickets even if the cost can be covered.
Selecting a preferred field of, say, twelve numbers from the available 49 numbers vastly reduces the total number of potential combinations, and brings such activity into a logistic and financial area of feasibility.
The elected field of say twelve numbers is then combed so as to give all possible combinations from the field, 924 for the specified number of picks, in this instance six, that forms each combination. Each combination is then entered on a respective ticket. Entering all combinations of six numbers from a chosen field of 12 numbers gives the guarantee that when all six winning numbers are among the chosen twelve, the highest prize will be awarded along with many other cash prizes. This complete combination of 12 numbers representing 924 combinations or groups or sets of six is commonly called 6 of 6. The following table shows minimum required numbers of tickets to ensure coverage for a specific combination form (reduced) and what is required for the correspondent minimum prize guaranteed.
______________________________________ Prize Group Nos. of tickets Guaranteed Winning Nos. to be entered on Prize among Nos. played play ______________________________________ 3 of 6 4 3 of 5 6 3 of 4 6 3 of 3 15 4 of 6 6 4 of 5 18 5 of 6 68 5 of 5 132 6 of 6 924 ______________________________________
In carrying out this operation, a number of aids have been previously available. Certain of these aids comprise random number generators; others include combination formulators.
From a search in the classified art the following listed U.S. patent references are considered to be of varying relevance to the present invention, being listed arbitrarily in numerical sequence, and not by relevance. The asterisked Reiss patent U.S. Pat. No. 4,712,796 is considered the most relevant.
U.S. Pat. No. 4,239,226, December 1980 PA1 U.S. Pat. No. 4,403,775, September 1983 PA1 U.S. Pat. No. 4,444,394, April 1984 PA1 U.S. Pat. No. 4,545,578, October 1985 PA1 U.S. Pat. No. 4,586,710, May 1986 PA1 U.S. Pat. No. 4,600,198, July 1986 PA1 U.S. Pat. No. 4,665,502, May 1987 PA1 U.S. Pat. No. 4,674,748, June 1987 PA1 U.S. Pat. No. 4,688,797, August 1987 PA1 U.S. Pat. No. 4,692,863, September 1987 PA1 U.S. Pat. No. 4,712,796, December 1987 PA1 U.S. Pat. No. 4,721,309, January 1988
Using the approach of a reduced field, the available number combinations can be mathematically derived by combinational analysis, as derived from scholarly sources ranging from "Arithmetica Practica" Herigone 1634 A.D. (now out of print) to "The VNR Concise Encyclopedia of Mathematics", page 577 published by Van Nostrand Reinhold Company 1977 A.D.
In the noted Reiss patent (U.S. Pat. No. '796) a single field of numbers can be dealt with at any time, using a rotary slide rule type of mechanism.
Another approach, using an appropriate mathematical table as referenced above and giving each selected actual number a sequential reference digit, then the combinations of reference digits for a field of given size, and for a pick of given extend, can be readily formulated from selected reference tables. The actual numbers then are substituted for the corresponding reference digits obtained from the combinational table, to yield the desired collection of combinations, which then can be individually transcribed onto lottery tickets. It will be seen that this is time consuming, tedious and boring, and is open to error, in view both of the transcription and the number-to-digit substitution that is necessary in such an operation.
The system disclosed in U.S. Pat. No. 4,712,796 comprises a mechanical device for providing combinations of six numbers selected from a field of twelve arbitrarily chosen numbers, with a guarantee prize of 4 of 6. This device may be used only one line at a time, such that both in making selections for the preparation of tickets, and in checking tickets for winning combinations, the operation can only be carried out for a single field at a time, which is exceedingly slow and tedious, as each cycle of operation requires erasure of the previous field and entry of a new, 12-digit field.
In accordance with the present invention a great number of alternative fields can be chosen and entered in a device at one time and the possible combinations for each field can be read off directly, one line at a time for each field, with the device being merely re indexed one line at a time, and the field re-read.
In another embodiment, a device is presented which allows the user to select any number of combinations from a large variety of fields.
In this concept the selector cards become united in a film transported against the field card, using a very simple indexing mechanism.